Diane Kruger and Joshua Jackson: Are They Engaged?

Could Diane Kruger and Joshua Jackson finally have decided to get hitched?

On Tuesday, the German-born actress stepped out in L.A. with Jackson, her boyfriend since 2006 – and she was wearing a very sparkly ring on that finger.

Of course, Kruger, 37, has previously sparked speculation with her choice of accessories. She's sported gems on her ring finger before, and in 2012, the couple shot down engagement rumors after Jackson bought her a $45,000 necklace at a charity auction in Monaco and reports claimed he was overheard saying it was an engagement present for Kruger.

But sources tell PEOPLE that Jackson, 35, has had marriage on his mind in recent months, and the former Fringe star has seemed ready to pop the question since last fall.

Reached by PEOPLE, her rep had no comment on the new engagement buzz.

Kruger, who stars on FX's The Bridge, and Jackson have said in the past that they were just fine staying happily unwed.

"Without being pessimistic, I learned that I don't believe in marriage," Kruger, who was divorced from French actor Guillaume Canet in 2006, told Glamour in 2011.

"I believe in a commitment that you make in your heart. There's no paper that will make you stay. A guy friend of mine said, and it made a lot of sense, that people should get married at the end of the road, not the beginning."